### Brain Teasers

# Romankachi Goodies !!!

Last week, I'd been to the famous Romankachi cookie store "Cookie World" and found that there were three types of cookies to my liking - kachie costing $11 each, chococook costing $7 each and peacon costing $8 each. I had spent any amount between $45 and $50 (Both values inclusive). In how many ways could I have purchased the items, if I wanted to purchase at least one of each type of cookie ?

### Answer

There are 6 ways.Since it is given that one item each has to be definitely bought, the minimum amount spent by me was $11 + $7 + $8 = $26. Using this minimum amount I should have bought at least one kachie, one chococook and one peacon cookies.

Since my total expenditure was $45 to $50, the extra amount I still have to spend (after having spent the minimum amount of $26) is $19 to $24, both $45 and $50 inclusive.

This extra amount can be spent in 6 possible ways as shown below :-

1) 2*11 = $22 (two kachie cookies).

2) 1*11 + 1*8 = $19 (one kachie cookie and one peacon cookie).

3) 2*7 + 1*8 = $22 (two chococook cookies and one peacon cookie).

4) 2*8 + 1*7 = $23 (two peacon cookies and one chococook cookie).

5) 7*3 = $21 (three chococook cookies)

6) 8*3 = $24 (three peacon cookies).

Hence there are six ways of spending the extra amount.

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